If the options in the mailman admin interface are set to "try to avoid duplicates" and every members is also set to "no duplicates", what are possible reasons if one of the subscribers receives each and every message twice?
Is it safe to say that it can't have anything to do with the list?
If this is happening to just one subscriber, I would say the likelihood is that they are either subscribed twice with two addresses that go to the same mailbox, or their mail server is doing something funny.
Ask said subscriber to send you all the headers for both messages. You should be able to tell the difference between them - it's possible that something along the way duplicated them, but the timestamps on headers normally makes it obvious.